Modeling of hypertension risk factors using local linear of additive nonparametric logistic regression

Abstract

Hypertension has become a serious health problem in Indonesia because of its prevalence, however, the causative factors could not be ascertained for about ninety percent of the patients. Various studies have found several risk factors causing hypertension to be obesity, family history, stress levels, heart rate, and an unhealthy lifestyle. In this case, the variables are considered influential on hypertension through a regression curve without a specific pattern. Also, we need to describe the functional relationships between several predictor variables with binary or dichotomous response variables and need to describe locally effect of predictor variables to the response variable. Therefore, in this study, to model the case of hypertension by age, body mass index, heart rate, stress levels we use the additive nonparametric logistic regression approach based on local linear estimators. The results of the study showed that hypertension was most prevalent among respondents over 65 years of age with BMI between 25-30 kg/m2 (obesity) and normal heart rate (60-100) bpm and most of them were found to be experiencing mild stress conditions. The model obtained a classification accuracy of 95 percent (in-sample) and 89.47 percent (out-sample) with a cut off probability value of 0.4.

Consistency and Asymptotic Normality of Estimator for Parameters in Multiresponse Multipredictor Semiparametric Regression Model

“…Finally, based on the truncated spline estimator proposed by [12] and by applying weighted least square (WLS) method, we can estimate the MMSR model presented by Equation (1). Next, we apply development of pivotal quantity method proposed by [43] to determine confidence interval for parameters in MMSR model.…”

“…By considering Equations ( 4) and ( 5), the estimation of a MMSR model presented by Equation (1) or Equation ( 2) based on truncated spline estimator is approximated by a linear function that is in the form of truncated spline with degree of polynomial 𝑑 = 1 (i.e., a linear polynomial) and knot point b and the number of knots B such that the MMSR model presented by Equation ( 1) can be expressed as follows:…”

“…In this section, we determine asymptotic normality of 𝛅 that is a truncated spline estimator for parameters of the MMSR model presented in Equation (1). Before investigating asymptotic normality of 𝛅, firstly we need to consider the following Lemma 2 and Theorem 3.…”

“…To estimate the regression function, there are several estimators which are frequently used in NR modeling; for example local linear, local polynomial, kernel, and spline. For prediction purposes, the use of local linear, local polynomial, and kernel estimators is highly recommended as discussed by [1][2][3][4][5][6][7][8][9][10][11]. Meanwhile, for prediction and interpretation purposes, the use of spline estimators is better and more flexible as discussed by [12][13][14].…”

The Prediction of Hypertension Risk

“…However, having a normal heart rate can still lead to hypertension in the presence of obesity [61]. [62] propose machine learning algorithms capable of predicting the presence of hypertension based on the analysis of instant heart rates. [63] verify the presence of a positive relationship between the growth of the heart rate and the risk of heart attack in hypertensive patients.…”